Model description

The model is a sum of three Gaussian peaks (elastic, breathing, bond-buckling), a DHO, and a linear function:

$$I(E) = I_{\text{elastic}}(E) + I_{\text{breathing}}(E) + I_{\text{magnon}}(E) + I_{\text{bond-buckling}}(E) + I_{\text{background}}(E)$$

Individual Components

1. Elastic Peak (First Gaussian)

$$I_{\text{elastic}}(E) = A_1 \exp\left(-\frac{(E - x_{1})^2}{2\sigma_1^2}\right)$$ where $\sigma_1 = \frac{\text{FWHM}_1}{2\sqrt{2\ln(2)}}$

2. Breathing Mode (Second Gaussian)

$$I_{\text{breathing}}(E) = A_2 \exp\left(-\frac{(E - x_{2})^2}{2\sigma_2^2}\right)$$ where $\sigma_2 = \frac{\text{FWHM}_2}{2\sqrt{2\ln(2)}}$

3. Magnon Peak (DHO)

$$I_{\text{magnon}}(E) = \frac{A_3 (\gamma E)^2}{(E^2 - x_3^2)^2 + (E \gamma)^2}$$ where $\gamma = \frac{\text{FWHM}_3}{2}$

4. Bond-buckling Mode (Fourth Gaussian)

$$I_{\text{bond-buckling}}(E) = A_4 \exp\left(-\frac{(E - x_{4})^2}{2\sigma_4^2}\right)$$ where $\sigma_4 = \frac{\text{FWHM}_4}{2\sqrt{2\ln(2)}}$

5. Linear Background

$$I_{\text{background}}(E) = \begin{cases} \text{slope} \cdot E & \text{if } E \geq 0 \\ 0 & \text{if } E < 0 \end{cases}$$

Parameters and Bounds

This section compares the temperature dependence of the elastic intensity, breathing intensity, breathing dispersion, bond-buckling intensity, and bond-buckling dispersion for LESCO 0.125.

• Colors: 15K (blue), 100K (cyan), 150K (gold), 200K (red)
• Circles: Breathing mode; Squares: Bond-buckling mode; Triangles: Elastic (divided by 1.5)